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AC-VOLTAGE REGULATORS M.Kaliamoorthy PSNACET

AC VOLTAGE CONTROLLER CIRCUITS

(RMS VOLTAGE CONTROLLERS)

AC voltage controllers (ac line voltage controllers) are employed to vary the RMS value

of the alternating voltage applied to a load circuit by introducing Thyristors between the load and

a constant voltage ac source. The RMS value of alternating voltage applied to a load circuit is

controlled by controlling the triggering angle of the Thyristors in the ac voltage controller

circuits.

In brief, an ac voltage controller is a type of thyristor power converter which is used to

convert a fixed voltage, fixed frequency ac input supply to obtain a variable voltage ac output.

The RMS value of the ac output voltage and the ac power flow to the load is controlled by

varying (adjusting) the trigger angle ‘’

ACVoltage

Controller

V0(RMS)

fS

Variable ACRMS O/P Voltage

ACInput

Voltagefs

Vs

fs

There are two different types of thyristor control used in practice to control the ac power flow

On-Off control

Phase control

These are the two ac output voltage control techniques.

In On-Off control technique Thyristors are used as switches to connect the load circuit to the

ac supply (source) for a few cycles of the input ac supply and then to disconnect it for few input

cycles. The Thyristors thus act as a high speed contactor (or high speed ac switch).

PHASE CONTROL

In phase control the Thyristors are used as switches to connect the load circuit to the

input ac supply, for a part of every input cycle. That is the ac supply voltage is chopped using

Thyristors during a part of each input cycle.


The thyristor switch is turned on for a part of every half cycle, so that input supply

voltage appears across the load and then turned off during the remaining part of input half cycle

to disconnect the ac supply from the load.

By controlling the phase angle or the trigger angle ‘’ (delay angle), the output RMS

voltage across the load can be controlled.

The trigger delay angle ‘’ is defined as the phase angle (the value of t) at which the

thyristor turns on and the load current begins to flow.

Thyristor ac voltage controllers use ac line commutation or ac phase commutation.

Thyristors in ac voltage controllers are line commutated (phase commutated) since the input

supply is ac. When the input ac voltage reverses and becomes negative during the negative half

cycle the current flowing through the conducting thyristor decreases and falls to zero. Thus the

ON thyristor naturally turns off, when the device current falls to zero.

Phase control Thyristors which are relatively inexpensive, converter grade Thyristors

which are slower than fast switching inverter grade Thyristors are normally used.

For applications upto 400Hz, if Triacs are available to meet the voltage and current

ratings of a particular application, Triacs are more commonly used.

Due to ac line commutation or natural commutation, there is no need of extra

commutation circuitry or components and the circuits for ac voltage controllers are very simple.

Due to the nature of the output waveforms, the analysis, derivations of expressions for

performance parameters are not simple, especially for the phase controlled ac voltage controllers

with RL load. But however most of the practical loads are of the RL type and hence RL load

should be considered in the analysis and design of ac voltage controller circuits.

TYPE OF AC VOLTAGE CONTROLLERS

The ac voltage controllers are classified into two types based on the type of input ac

supply applied to the circuit.

Single Phase AC Controllers.

Three Phase AC Controllers.

Single phase ac controllers operate with single phase ac supply voltage of 230V RMS at

50Hz in our country. Three phase ac controllers operate with 3 phase ac supply of 400V RMS at

50Hz supply frequency.

Each type of controller may be sub divided into


Uni-directional or half wave ac controller.

Bi-directional or full wave ac controller.

In brief different types of ac voltage controllers are

Single phase half wave ac voltage controller (uni-directional controller).

Single phase full wave ac voltage controller (bi-directional controller).

Three phase half wave ac voltage controller (uni-directional controller).

Three phase full wave ac voltage controller (bi-directional controller).

APPLICATIONS OF AC VOLTAGE CONTROLLERS

Lighting / Illumination control in ac power circuits.

Induction heating.

Industrial heating & Domestic heating.

Transformer tap changing (on load transformer tap changing).

Speed control of induction motors (single phase and poly phase ac induction motor

control).

AC magnet controls.

PRINCIPLE OF ON-OFF CONTROL TECHNIQUE (INTEGRAL CYCLE CONTROL)

The basic principle of on-off control technique is explained with reference to a single

phase full wave ac voltage controller circuit shown below. The thyristor switches 1T and 2T are

turned on by applying appropriate gate trigger pulses to connect the input ac supply to the load

for ‘n’ number of input cycles during the time interval ONt . The thyristor switches 1T and 2T are

turned off by blocking the gate trigger pulses for ‘m’ number of input cycles during the time

interval OFFt . The ac controller ON time ONt usually consists of an integral number of input

cycles.


LR R = Load ResistanceFig.: Single phase full wave AC voltage controller circuit

Vs

Vo

io

ig1

ig2

wt

wt

wt

wt

Gate pulse of T1

Gate pulse of T2

n m

Fig.: WaveformsExample

Referring to the waveforms of ON-OFF control technique in the above diagram,


n Two input cycles. Thyristors are turned ON during ONt for two input cycles.

m One input cycle. Thyristors are turned OFF during OFFt for one input cycle

Fig.: Power Factor

Thyristors are turned ON precisely at the zero voltage crossings of the input supply. The

thyristor 1T is turned on at the beginning of each positive half cycle by applying the gate trigger

pulses to 1T as shown, during the ON time ONt . The load current flows in the positive direction,

which is the downward direction as shown in the circuit diagram when 1T conducts. The thyristor

2T is turned on at the beginning of each negative half cycle, by applying gating signal to the gate

of 2T , during ONt . The load current flows in the reverse direction, which is the upward direction

when 2T conducts. Thus we obtain a bi-directional load current flow (alternating load current

flow) in a ac voltage controller circuit, by triggering the thyristors alternately.

This type of control is used in applications which have high mechanical inertia and high

thermal time constant (Industrial heating and speed control of ac motors). Due to zero voltage

and zero current switching of Thyristors, the harmonics generated by switching actions are

reduced.

For a sine wave input supply voltage,

sin 2 sins m Sv V t V t

SV RMS value of input ac supply =2mV

= RMS phase supply voltage.


If the input ac supply is connected to load for ‘n’ number of input cycles and

disconnected for ‘m’ number of input cycles, then

,ON OFFt n T t m T

Where1

Tf

= input cycle time (time period) and

f = input supply frequency.

ONt = controller on time = n T .

OFFt = controller off time = m T .

OT = Output time period = ON OFFt t nT mT .

We can show that,

Output RMS voltage ON ON

SO RMS i RMSO O

t tV V V

T T

Where i RMSV is the RMS input supply voltage = SV .

TO DERIVE AN EXPRESSION FOR THE RMS VALUE OF OUTPUT VOLTAGE, FOR

ON-OFF CONTROL METHOD.

Output RMS voltage 2 2

0

1.

ONt

mO RMSO t

V V Sin t d tT

2

2

0

.ONt

mO RMS

O

VV Sin t d t

T

Substituting for 2 1 2

2

CosSin

2

0

1 2

2

ONt

mO RMS

O

V Cos tV d t

T

2

0 0

2 .2

ON ONt t

mO RMS

O

VV d t Cos t d t

T

2

0 0

222

ON ONt tm

O RMSO

V Sin tV t

T


2 sin 2 sin 0

02 2

m ONONO RMS

O

V tV t

T

Now ONt = An integral number of input cycles; Hence

, 2 ,3 , 4 ,5 ,.....ONt T T T T T & 2 , 4 ,6 ,8 ,10 ,......ONt

Where T is the input supply time period (T = input cycle time period). Thus we note that

sin 2 0ONt

2

2 2m ON m ON

O RMSO O

V t V tV

T T

ON ON

SO RMS i RMSO O

t tV V V

T T

Where 2m

Si RMS

VV V = RMS value of input supply voltage;

ON ON

O ON OFF

t t nT nk

T t t nT mT n m

= duty cycle (d).

S SO RMS

nV V V k

m n

PERFORMANCE PARAMETERS OF AC VOLTAGE CONTROLLERS

RMS Output (Load) Voltage

1

222 2

0

sin .2 mO RMS

nV V t d t

n m

2m

SO RMS i RMS

V nV V k V k

m n

SO RMS i RMSV V k V k

Where S i RMSV V = RMS value of input supply voltage.

Duty Cycle

ON ON

O ON OFF

t t nTk

T t t m n T


Where,

nk

m n

= duty cycle (d).

RMS Load Current

O RMS O RMS

O RMSL

V VI

Z R ; for a resistive load LZ R .

Output AC (Load) Power

2

O LO RMSP I R

Input Power Factor

output load power

input supply volt amperesO O

S S

P PPF

VA V I

2LO RMS

i RMS in RMS

I RPF

V I

; S in RMSI I RMS input supply current.

The input supply current is same as the load current in O LI I I

Hence, RMS supply current = RMS load current; in RMS O RMSI I .

2LO RMS O RMS i RMS

i RMS in RMS i RMS i RMS

I R V V kPF k

V I V V

nPF k

m n

The Average Current of Thyristor T AvgI

0 2 3 t

Im

nmiT

Waveform of Thyristor Current


0

sin .2 mT Avg

nI I t d t

m n

0

sin .2

mT Avg

nII t d t

m n

0

cos2

mT Avg

nII t

m n

cos cos 02

mT Avg

nII

m n

1 12

mT Avg

nII

m n

22 mT Avg

nI I

m n

.m m

T Avg

I n k II

m n

duty cycle ON

ON OFF

t nk

t t n m

.m m

T Avg

I n k II

m n

,

Where mm

L

VI

R = maximum or peak thyristor current.

RMS Current of Thyristor T RMSI

1

22 2

0

sin .2 mT RMS

nI I t d t

n m

1

222

0

sin .2

mT RMS

nII t d t

n m

122

0

1 cos 2

2 2m

T RMS

tnII d t

n m


1

22

0 0

cos 2 .4

mT RMS

nII d t t d t

n m

1

22

0 0

sin 224

mT RMS

nI tI t

n m

1

22 sin 2 sin 00

4 2m

T RMS

nII

n m

1

22

0 04

mT RMS

nII

n m

1 12 22 2

4 4m m

T RMS

nI nII

n m n m

2 2m m

T RMS

I InI k

m n

2m

T RMS

II k

PRINCIPLE OF AC PHASE CONTROL

The basic principle of ac phase control technique is explained with reference to a single

phase half wave ac voltage controller (unidirectional controller) circuit shown in the below

figure. The half wave ac controller uses one thyristor and one diode connected in parallel across

each other in opposite direction that is anode of thyristor 1T is connected to the cathode of diode

1D and the cathode of 1T is connected to the anode of 1D . The output voltage across the load

resistor ‘R’ and hence the ac power flow to the load is controlled by varying the trigger angle

‘’. The trigger angle or the delay angle ‘’ refers to the value of t or the instant at which the

thyristor 1T is triggered to turn it ON, by applying a suitable gate trigger pulse between the gate

and cathode lead.The thyristor 1T is forward biased during the positive half cycle of input ac

supply. It can be triggered and made to conduct by applying a suitable gate trigger pulse only

during the positive half cycle of input supply. When 1T is triggered it conducts and the load

current flows through the thyristor 1T , the load and through the transformer secondary winding.


By assuming 1T as an ideal thyristor switch it can be considered as a closed switch when

it is ON during the period t to radians. The output voltage across the load follows the

input supply voltage when the thyristor 1T is turned-on and when it conducts from t to

radians. When the input supply voltage decreases to zero at t , for a resistive load the

load current also falls to zero at t and hence the thyristor 1T turns off at t . Between

the time period t to 2 , when the supply voltage reverses and becomes negative the diode

1D becomes forward biased and hence turns ON and conducts. The load current flows in the

opposite direction during t to 2 radians when 1D is ON and the output voltage follows

the negative half cycle of input supply.

Fig.: Halfwave AC phase controller (Unidirectional Controller)


Equations

Input AC Supply Voltage across the Transformer Secondary Winding.

sins mv V t

2m

S in RMS

VV V = RMS value of secondary supply voltage.

Output Load Voltage

0o Lv v ; for 0t to

sino L mv v V t ; for t to 2 .

Output Load Current

sino mo L

L L

v V ti i

R R

; for t to 2 .

0o Li i ; for 0t to .

TO DERIVE AN EXPRESSION FOR RMS OUTPUT VOLTAGE O RMSV

2

2 21sin .

2 mO RMSV V t d t

22 1 cos 2

.2 2

mO RMS

V tV d t

22

1 cos 2 .4

mO RMS

VV t d t

2 2

cos 2 .2

mO RMS

VV d t t d t

2 2sin 2

22m

O RMS

V tV t

2sin 2

222

mO RMS

V tV

sin 4 sin 22 ;sin 4 0

2 22m

O RMS

VV


sin 22

22m

O RMS

VV

sin 22

22 2m

O RMS

VV

1 sin 22

2 22m

O RMS

VV

1 sin 22

2 2O RMS i RMSV V

1 sin 22

2 2SO RMSV V

Where, 2m

Si RMS

VV V = RMS value of input supply voltage (across the transformer

secondary winding).

Note: Output RMS voltage across the load is controlled by changing ' ' as indicated by the

expression for O RMSV

PLOT OF O RMSV VERSUS TRIGGER ANGLE FOR A SINGLE PHASE HALF-WAVE

AC VOLTAGE CONTROLLER (UNIDIRECTIONAL CONTROLLER)

1 sin 22

2 22m

O RMS

VV

1 sin 22

2 2SO RMSV V

By using the expression for O RMSV we can obtain the control characteristics, which is the

plot of RMS output voltage O RMSV versus the trigger angle . A typical control characteristic

of single phase half-wave phase controlled ac voltage controller is as shown below

Trigger angle in degrees

Trigger angle in radians

O RMSV

0 02m

S

VV

030 6 1; 6

0.992765 SV


060 3 2; 6

0.949868 SV

090 2 3; 6

0.866025 SV

0120 23

4; 6 0.77314 SV

0150 56

5; 6 0.717228 SV

0180 6; 6 0.707106 SV

VO(RMS)


0 60 120 180

100% VS

20% VS

60% VS

70.7% VS

Fig.: Control characteristics of single phase half-wave phase controlled ac voltage

controller

Note: We can observe from the control characteristics and the table given above that the range of

RMS output voltage control is from 100% of SV to 70.7% of SV when we vary the trigger angle

from zero to 180 degrees. Thus the half wave ac controller has the draw back of limited range

RMS output voltage control.

TO CALCULATE THE AVERAGE VALUE (DC VALUE) OF OUTPUT VOLTAGE

21

sin .2 mO dcV V t d t

2

sin .2

mO dc

VV t d t

2

cos2

mO dc

VV t


cos 2 cos2

mO dc

VV

; cos 2 1

cos 12

mdc

VV

; 2m SV V

Hence 2cos 1

2S

dc

VV

When ' ' is varied from 0 to . dcV varies from 0 to mV

DISADVANTAGES OF SINGLE PHASE HALF WAVE AC VOLTAGE CONTROLLER.

The output load voltage has a DC component because the two halves of the output

voltage waveform are not symmetrical with respect to ‘0’ level. The input supply current

waveform also has a DC component (average value) which can result in the problem of

core saturation of the input supply transformer.

The half wave ac voltage controller using a single thyristor and a single diode provides

control on the thyristor only in one half cycle of the input supply. Hence ac power flow to

the load can be controlled only in one half cycle.

Half wave ac voltage controller gives limited range of RMS output voltage control.

Because the RMS value of ac output voltage can be varied from a maximum of 100% of

SV at a trigger angle 0 to a low of 70.7% of SV at Radians .

These drawbacks of single phase half wave ac voltage controller can be over come by using a

single phase full wave ac voltage controller.

APPLICATIONS OF RMS VOLTAGE CONTROLLER

Speed control of induction motor (poly phase ac induction motor).

Heater control circuits (industrial heating).

Welding power control.

Induction heating.

On load transformer tap changing.

Lighting control in ac circuits.

Ac magnet controls.


SINGLE PHASE FULL WAVE AC VOLTAGE CONTROLLER (AC REGULATOR) ORRMS VOLTAGE CONTROLLER WITH RESISTIVE LOAD

Single phase full wave ac voltage controller circuit using two SCRs or a single triac is

generally used in most of the ac control applications. The ac power flow to the load can be

controlled in both the half cycles by varying the trigger angle ' ' .

The RMS value of load voltage can be varied by varying the trigger angle ' ' . The input

supply current is alternating in the case of a full wave ac voltage controller and due to the

symmetrical nature of the input supply current waveform there is no dc component of input

supply current i.e., the average value of the input supply current is zero.

A single phase full wave ac voltage controller with a resistive load is shown in the figure

below. It is possible to control the ac power flow to the load in both the half cycles by adjusting

the trigger angle ' ' . Hence the full wave ac voltage controller is also referred to as to a bi-

directional controller.

Fig.: Single phase full wave ac voltage controller (Bi-directional Controller) using SCRs

The thyristor 1T is forward biased during the positive half cycle of the input supply

voltage. The thyristor 1T is triggered at a delay angle of ' ' 0 radians . Considering

the ON thyristor 1T as an ideal closed switch the input supply voltage appears across the load

resistor LR and the output voltage O Sv v during t to radians. The load current flows

through the ON thyristor 1T and through the load resistor LR in the downward direction during

the conduction time of 1T from t to radians.


At t , when the input voltage falls to zero the thyristor current (which is flowing

through the load resistor LR ) falls to zero and hence 1T naturally turns off . No current flows in

the circuit during t to . The thyristor 2T is forward biased during the negative

cycle of input supply and when thyristor 2T is triggered at a delay angle , the output

voltage follows the negative halfcycle of input from t to 2 . When 2T is ON, the

load current flows in the reverse direction (upward direction) through 2T during t to

2 radians. The time interval (spacing) between the gate trigger pulses of 1T and 2T is kept at

radians or 1800. At 2t the input supply voltage falls to zero and hence the load current

also falls to zero and thyristor 2T turn off naturally.

Instead of using two SCR’s in parallel, a Triac can be used for full wave ac voltage control.

Fig.: Single phase full wave ac voltage controller (Bi-directional Controller) using TRIAC

Fig: Waveforms of single phase full wave ac voltage controller


EQUATIONSInput supply voltage

sin 2 sinS m Sv V t V t ;

Output voltage across the load resistor LR ;

sinO L mv v V t ;

for tot and to 2t

Output load currentsin

sinO mO m

L L

v V ti I t

R R

;

for tot and to 2t

TO DERIVE AN EXPRESSION FOR THE RMS VALUE OF OUTPUT (LOAD)VOLTAGE

The RMS value of output voltage (load voltage) can be found using the expression

2

2 2 2

0

1

2 LO RMS L RMSV V v d t

;

For a full wave ac voltage controller, we can see that the two half cycles of output voltage

waveforms are symmetrical and the output pulse time period (or output pulse repetition time) is

radians. Hence we can also calculate the RMS output voltage by using the expression given

below.

2 2 2

0

1sin .mL RMSV V t d t

2

2 2

0

1.

2 LL RMSV v d t

;

sinL O mv v V t ; For tot and to 2t

Hence,

2

2 22 1sin sin

2 m mL RMSV V t d t V t d t

2

2 2 2 21sin . sin .

2 m mV t d t V t d t

22 1 cos 2 1 cos 2

2 2 2mV t t

d t d t


2 22

cos 2 . cos 2 .2 2

mVd t t d t d t t d t

2 22 sin 2 sin 2

4 2 2mV t t

t t

2 1 1

sin 2 sin 2 sin 4 sin 24 2 2

mV

2 1 1

2 0 sin 2 0 sin 24 2 2

mV

2 sin 2sin 22

4 2 2mV

2 sin 2 2sin 22

4 2 2mV

2 sin 2 1

2 sin 2 .cos 2 cos 2 .sin 24 2 2

mV

sin 2 0 & cos 2 1

Therefore,

2

2 sin 2 sin 22

4 2 2m

L RMS

VV

2

2 sin 24

mV

2

2 2 2 sin 24

mL RMS

VV

Taking the square root, we get

2 2 sin 22

mL RMS

VV

2 2 sin 22 2

mL RMS

VV

12 2 sin 2

22m

L RMS

VV


1 sin 22

2 22m

L RMS

VV

1 sin 2

22m

L RMS

VV

1 sin 2

2L RMS i RMSV V

1 sin 2

2SL RMSV V

Maximum RMS voltage will be applied to the load when 0 , in that case the full sine

wave appears across the load. RMS load voltage will be the same as the RMS supply

voltage2mV

. When is increased the RMS load voltage decreases.

0

1 sin 2 00

22m

L RMS

VV

0

1 0

22m

L RMS

VV

0 2

mSL RMS i RMS

VV V V

The output control characteristic for a single phase full wave ac voltage controller with

resistive load can be obtained by plotting the equation for O RMSV

CONTROL CHARACTERISTIC OF SINGLE PHASE FULL-WAVE AC VOLTAGE

CONTROLLER WITH RESISTIVE LOAD

The control characteristic is the plot of RMS output voltage O RMSV versus the trigger angle ;

which can be obtained by using the expression for the RMS output voltage of a full-wave ac

controller with resistive load.

1 sin 2

2SO RMSV V

;


Where2m

S

VV RMS value of input supply voltage


Trigger angle in radians O RMSV %

0 0 SV 100% SV

030 6 1; 6

0.985477 SV 98.54% SV

060 3 2; 6

0.896938 SV 89.69% SV

090 2 3; 6

0.7071 SV 70.7% SV

0120 23

4; 6 0.44215 SV 44.21% SV

0150 56

5; 6 0.1698 SV 16.98% SV

0180 6; 6 0 SV 0 SV

VO(RMS)


0 60 120 180

VS

0.2 VS

0.6VS

We can notice from the figure, that we obtain a much better output control characteristic

by using a single phase full wave ac voltage controller. The RMS output voltage can be varied

from a maximum of 100% SV at 0 to a minimum of ‘0’ at 0180 . Thus we get a full

range output voltage control by using a single phase full wave ac voltage controller.

Need For Isolation

In the single phase full wave ac voltage controller circuit using two SCRs or Thyristors

1T and 2T in parallel, the gating circuits (gate trigger pulse generating circuits) of Thyristors 1T


and 2T must be isolated. Figure shows a pulse transformer with two separate windings to provide

isolation between the gating signals of 1T and 2T .

G1

K1G2

K2

GateTriggerPulse

Generator

Fig.: Pulse Transformer

SINGLE PHASE FULL-WAVE AC VOLTAGE CONTROLLER WITH COMMON

CATHODE

It is possible to design a single phase full wave ac controller with a common cathode

configuration by having a common cathode point for 1T and 2T & by adding two diodes in a full

wave ac controller circuit as shown in the figure below

Fig.: Single phase full wave ac controller with common cathode(Bidirectional controller in common cathode configuration)

Thyristor 1T and diode 1D are forward biased during the positive half cycle of input

supply. When thyristor 1T is triggered at a delay angle , Thyristor 1T and diode 1D conduct

together from t to during the positive half cycle.


The thyristor 2T and diode 2D are forward biased during the negative half cycle of input

supply, when trigged at a delay angle , thyristor 2T and diode 2D conduct together during the

negative half cycle from t to 2 .

In this circuit as there is one single common cathode point, routing of the gate trigger

pulses to the thyristor gates of 1T and 2T is simpler and only one isolation circuit is required.

But due to the need of two power diodes the costs of the devices increase. As there are

two power devices conducting at the same time the voltage drop across the ON devices increases

and the ON state conducting losses of devices increase and hence the efficiency decreases.

SINGLE PHASE FULL WAVE AC VOLTAGE CONTROLLER USING A SINGLE

THYRISTOR

RL

T1

ACSupply

-

D1

D4

D3

D2

+

A single phase full wave ac controller can also be implemented with one thyristor and

four diodes connected in a full wave bridge configuration as shown in the above figure. The four

diodes act as a bridge full wave rectifier. The voltage across the thyristor 1T and current through

thyristor 1T are always unidirectional. When 1T is triggered at t , during the positive half

cycle 0 , the load current flows through 1D , 1T , diode 2D and through the load. With a

resistive load, the thyristor current (flowing through the ON thyristor 1T ) , the load current falls

to zero at t , when the input supply voltage decreases to zero at t , the thyristor

naturally turns OFF.


In the negative half cycle, diodes 3 4&D D are forward biased during

to 2t radians. When 1T is triggered at t , the load current flows in the

opposite direction (upward direction) through the load, through 3D , 1T and 4D . Thus 3D , 4D and

1T conduct together during the negative half cycle to supply the load power. When the input

supply voltage becomes zero at 2t , the thyristor current (load current) falls to zero at

2t and the thyristor 1T naturally turns OFF. The waveforms and the expression for the

RMS output voltage are the same as discussed earlier for the single phase full wave ac controller.

But however if there is a large inductance in the load circuit, thyristor 1T may not be

turned OFF at the zero crossing points, in every half cycle of input voltage and this may result in

a loss of output control. This would require detection of the zero crossing of the load current

waveform in order to ensure guaranteed turn off of the conducting thyristor before triggering the

thyristor in the next half cycle, so that we gain control on the output voltage.

In this full wave ac controller circuit using a single thyristor, as there are three power

devices conducting together at the same time there is more conduction voltage drop and an

increase in the ON state conduction losses and hence efficiency is also reduced.

The diode bridge rectifier and thyristor (or a power transistor) act together as a

bidirectional switch which is commercially available as a single device module and it has

relatively low ON state conduction loss. It can be used for bidirectional load current control and

for controlling the RMS output voltage.

SINGLE PHASE FULL WAVE AC VOLTAGE CONTROLLER (BIDIRECTIONAL

CONTROLLER) WITH RL LOAD

In this section we will discuss the operation and performance of a single phase full wave

ac voltage controller with RL load. In practice most of the loads are of RL type. For example if

we consider a single phase full wave ac voltage controller controlling the speed of a single phase

ac induction motor, the load which is the induction motor winding is an RL type of load, where

R represents the motor winding resistance and L represents the motor winding inductance.

A single phase full wave ac voltage controller circuit (bidirectional controller) with an

RL load using two thyristors 1T and 2T ( 1T and 2T are two SCRs) connected in parallel is shown


in the figure below. In place of two thyristors a single Triac can be used to implement a full wave

ac controller, if a suitable Traic is available for the desired RMS load current and the RMS

output voltage ratings.

Fig: Single phase full wave ac voltage controller with RL load

The thyristor 1T is forward biased during the positive half cycle of input supply. Let us

assume that 1T is triggered at t , by applying a suitable gate trigger pulse to 1T during the

positive half cycle of input supply. The output voltage across the load follows the input supply

voltage when 1T is ON. The load current Oi flows through the thyristor 1T and through the load in

the downward direction. This load current pulse flowing through 1T can be considered as the

positive current pulse. Due to the inductance in the load, the load current Oi flowing through 1T

would not fall to zero at t , when the input supply voltage starts to become negative.

The thyristor 1T will continue to conduct the load current until all the inductive energy

stored in the load inductor L is completely utilized and the load current through 1T falls to zero at

t , where is referred to as the Extinction angle, (the value of t ) at which the load

current falls to zero. The extinction angle is measured from the point of the beginning of the

positive half cycle of input supply to the point where the load current falls to zero.

The thyristor 1T conducts from t to . The conduction angle of 1T is ,

which depends on the delay angle and the load impedance angle . The waveforms of the

input supply voltage, the gate trigger pulses of 1T and 2T , the thyristor current, the load current

and the load voltage waveforms appear as shown in the figure below.


Fig.: Input supply voltage & Thyristor current waveforms

is the extinction angle which depends upon the load inductance value.

Fig.: Gating Signals


Waveforms of single phase full wave ac voltage controller with RL load for .

Discontinuous load current operation occurs for and ;

i.e., , conduction angle .

Fig.: Waveforms of Input supply voltage, Load Current, Load Voltage and ThyristorVoltage across 1T

Note


The RMS value of the output voltage and the load current may be varied by varying the

trigger angle .

This circuit, AC RMS voltage controller can be used to regulate the RMS voltage across

the terminals of an ac motor (induction motor). It can be used to control the temperature

of a furnace by varying the RMS output voltage.

For very large load inductance ‘L’ the SCR may fail to commutate, after it is triggered

and the load voltage will be a full sine wave (similar to the applied input supply voltage

and the output control will be lost) as long as the gating signals are applied to the

thyristors 1T and 2T . The load current waveform will appear as a full continuous sine

wave and the load current waveform lags behind the output sine wave by the load power

factor angle .

TO DERIVE AN EXPRESSION FOR THE OUTPUT (INDUCTIVE LOAD) CURRENT,

DURING tot WHEN THYRISTOR 1T CONDUCTS

Considering sinusoidal input supply voltage we can write the expression for the

supply voltage as

sinS mv V t = instantaneous value of the input supply voltage.

Let us assume that the thyristor 1T is triggered by applying the gating signal to 1T at

t . The load current which flows through the thyristor 1T during t to can be found

from the equation

sinOO m

diL Ri V t

dt

;

The solution of the above differential equation gives the general expression for the output

load current which is of the form

1sint

mO

Vi t A e

Z

;

Where 2m SV V = maximum or peak value of input supply voltage.

22Z R L = Load impedance.

1tanL

R

= Load impedance angle (power factor angle of load).


L

R = Load circuit time constant.

Therefore the general expression for the output load current is given by the equation

1sinR

tm L

O

Vi t A e

Z

;

The value of the constant 1A can be determined from the initial condition. i.e. initial

value of load current 0Oi , at t . Hence from the equation for Oi equating Oi to zero and

substituting t , we get

10 sinR

tm L

O

Vi A e

Z

Therefore 1 sinR

tmL

VA e

Z

1

1sinm

Rt

L

VA

Ze

1 sinR

tmL

VA e

Z

1 sinR t

mLV

A eZ

By substituting t , we get the value of constant 1A as

1 sinR

mLV

A eZ

Substituting the value of constant 1A from the above equation into the expression for Oi , we

obtain

sin sinRR

tm mLL

O

V Vi t e e

Z Z

;

sin sinR t R

m mL LO

V Vi t e e

Z Z


sin sinR

tm mL

O

V Vi t e

Z Z

Therefore we obtain the final expression for the inductive load current of a single phase

full wave ac voltage controller with RL load as

sin sin

Rt

m LO

Vi t e

Z

; Where t .

The above expression also represents the thyristor current 1Ti , during the conduction time

interval of thyristor 1T from tot .

To Calculate Extinction Angle

The extinction angle , which is the value of t at which the load current Oi falls

to zero and 1T is turned off can be estimated by using the condition that 0Oi , at t

By using the above expression for the output load current, we can write

0 sin sin

Rm L

O

Vi e

Z

As 0mV

Z we can write

sin sin 0

R

Le

Therefore we obtain the expression

sin sin

R

Le

The extinction angle can be determined from this transcendental equation by using the

iterative method of solution (trial and error method). After is calculated, we can determine the

thyristor conduction angle .

is the extinction angle which depends upon the load inductance value. Conduction

angle increases as is decreased for a known value of .

For radians, i.e., for radians, for the load current

waveform appears as a discontinuous current waveform as shown in the figure. The output load


current remains at zero during t to . This is referred to as discontinuous load

current operation which occurs for .

When the trigger angle is decreased and made equal to the load impedance angle

i.e., when we obtain from the expression for sin ,

sin 0 ; Therefore radians.

Extinction angle ; for the case when

Conduction angle 0 radians 180 ; for the case when

Each thyristor conducts for 1800 ( radians ) . 1T conducts from t to and

provides a positive load current. 2T conducts from to 2 and provides a negative

load current. Hence we obtain a continuous load current and the output voltage waveform

appears as a continuous sine wave identical to the input supply voltage waveform for trigger

angle and the control on the output is lost.

vO

2

3

t

Vm

0

Im

t

v =vO S

iO

Fig.: Output voltage and output current waveforms for a single phase full wave ac voltagecontroller with RL load for

Thus we observe that for trigger angle , the load current tends to flow continuously

and we have continuous load current operation, without any break in the load current waveform

and we obtain output voltage waveform which is a continuous sinusoidal waveform identical to


the input supply voltage waveform. We loose the control on the output voltage for as the

output voltage becomes equal to the input supply voltage and thus we obtain

2m

SO RMS

VV V ; for

Hence,

RMS output voltage = RMS input supply voltage for

TO DERIVE AN EXPRESSION FOR RMS OUTPUT VOLTAGE O RMSV OF A SINGLE

PHASE FULL-WAVE AC VOLTAGE CONTROLLER WITH RL LOAD.

When O , the load current and load voltage waveforms become discontinuous asshown in the figure above.

1

22 21sin .mO RMSV V t d t

Output sino mv V t , for tot , when 1T is ON.

122 1 cos 2

2m

O RMS

tVV d t

1

22

cos 2 .2

mO RMS

VV d t t d t

1

22 sin 222

mO RMS

V tV t

1

2 2sin 2 sin 2

2 2 2m

O RMS

VV


1

21 sin 2 sin 2

2 2 2mO RMSV V

1

21 sin 2 sin 2

2 22m

O RMS

VV

The RMS output voltage across the load can be varied by changing the trigger angle .

For a purely resistive load 0L , therefore load power factor angle 0 .

1tan 0L

R

;

Extinction angle 0 radians 180

PERFORMANCE PARAMETERS OF A SINGLE PHASE FULL WAVE AC VOLTAGE

CONTROLLER WITH RESISTIVE LOAD

RMS Output Voltage 1 sin 2

22m

O RMS

VV

;2m

S

VV = RMS input

supply voltage.

O RMS

O RMSL

VI

R = RMS value of load current.

S O RMSI I = RMS value of input supply current.

Output load power

2

O LO RMSP I R

Input Power Factor

2

L LO RMS O RMSO

S S S SO RMS

I R I RPPF

V I V I V

1 sin 2

2O RMS

S

VPF

V

Average Thyristor Current,


Im

iT1

2 (2 + )

3

t

Fig.: Thyristor Current Waveform

1 1sin .

2 2T mT AvgI i d t I t d t

sin . cos2 2

m mT Avg

I II t d t t

cos cos 1 cos2 2

m mT Avg

I II

Maximum Average Thyristor Current, for 0 ,

m

T Avg

II

RMS Thyristor Current

2 21sin .

2 mT RMSI I t d t

1 sin 2

2 22m

T RMS

II

Maximum RMS Thyristor Current, for 0 ,

2m

T RMS

II

In the case of a single phase full wave ac voltage controller circuit using a Triac with

resistive load, the average thyristor current 0T AvgI . Because the Triac conducts in both the

half cycles and the thyristor current is alternating and we obtain a symmetrical thyristor current

waveform which gives an average value of zero on integration.


PERFORMANCE PARAMETERS OF A SINGLE PHASE FULL WAVE AC VOLTAGE

CONTROLLER WITH R-L LOAD

The Expression for the Output (Load) CurrentThe expression for the output (load) current which flows through the thyristor, during tot is given by

1

sin sinR

tm L

O T

Vi i t e

Z

; for t

Where,

2m SV V = Maximum or peak value of input ac supply voltage.

22Z R L = Load impedance.

1tanL

R

= Load impedance angle (load power factor angle).

= Thyristor trigger angle = Delay angle.

= Extinction angle of thyristor, (value of t ) at which the thyristor (load) current fallsto zero.

is calculated by solving the equation

sin sin

R

Le

Thyristor Conduction Angle

Maximum thyristor conduction angle radians = 1800 for .

RMS Output Voltage

1 sin 2 sin 2

2 22m

O RMS

VV

The Average Thyristor Current

1

1

2 TT AvgI i d t

1sin sin

2

Rt

m LT Avg

VI t e d t

Z


sin . sin2

Rt

m LT Avg

VI t d t e d t

Z

Maximum value of T AvgI occur at 0 . The thyristors should be rated for maximum

m

T Avg

II

, where mm

VI

Z .

RMS Thyristor Current T RMSI

1

21

2 TT RMSI i d t

Maximum value of T RMSI occurs at 0 . Thyristors should be rated for maximum

2m

T RMS

II

When a Triac is used in a single phase full wave ac voltage controller with RL type of

load, then 0T AvgI and maximum 2m

T RMS

II

ac voltage controller circuits (rms …kaliasgoldmedal.yolasite.com/resources/power_electronics/ac...

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